Cold atoms may offer fundamentally new insights into quantum many-body physics, not only due to their extreme tunability, but also thanks to the new probes that they give access to. One such probe is noise, either local in momentum space (via time-of-flight images) or in real space (via in-situ images). In this talk I will first discuss how noise in momentum space can serve as an invaluable tool for thermometry via fluctuation-dissipation relations, generally valid for classical systems; moreover, the violation of such relations for quantum systems provides new insight into the structure of quantum fluctuations in momentum space. On the other hand, noise in real space -- in the form of local density fluctuations -- is a manifestation of entanglement between a part of an extended quantum system and its complement. Focusing on the case of free fermions and of Bose-condensed interacting bosons, I will discuss how fluctuations and entanglement entropy may obey the same scaling law (for fermions); as well as obey different scaling laws (for bosons) due to a fundamental discrepancy between the spatial structure of entanglement and that of measurable correlations.